Physically, what is this?

Philips Pavilion, where one was to experience the poem, was designed as a celebration of the technological progress made after World War II. Philips, an electronics company in the Netherlands, commissioned Charles-Édouard Jeanneret, who is also known as Le Corbusier, to build the pavilion, that would eventually house this spectacle.  Le Corbusier was a Swedish architect and painter, who was known for his "modern architecture." 

Le Corbusier envisioned that it would be a "poem in a bottle," which is thus reflected in its architecture.  The "building" is comprised of nine hyperbolic structures or paraboloids to create the a-symmetrical,  cylindrical, almost cone-like shape.

Interestingly enough, Pringle chips are an example of hyperbolic paraboloids.